# Anisotropic evolution of 4-brane in a 6D generalized Randall-Sundrum model

## TL;DR

This paper explores a 6D generalized Randall-Sundrum brane world model with anisotropic metrics, showing it can produce a universe with exponential expansion and a positive cosmological constant, addressing dark energy.

## Contribution

It introduces an anisotropic metric ansatz in a 6D brane model, deriving cosmological solutions that include exponential expansion and a positive effective cosmological constant.

## Key findings

- Universe expansion proportional to t^{1/2} during radiation era
- Effective cosmological constant is positive and independent of integration constants
- Model supports exponential expansion consistent with current observations

## Abstract

We investigate a 6d generalized Randall-Sundrum brane world scenario with a bulk cosmological constant. It is shown that each stress-energy tensor $T_{ab}^{i}$ on the brane is similar to a constant vacuum energy. This is consistent with the Randall-Sundrum model in which each 3-brane Lagrangian separated out a constant vacuum energy. By adopting an anisotropic metric ansatz, we obtain the 5d Friedmann-Robertson-Walker field equations. At a little later period, the expansion of the universe is proportional to $t^{\frac{1}{2}}$ which is as similar as the period of the radiation-dominated. We also investigate the case with two $a(t)$ and two $b(t)$. In a large region of $t$, we obtain the 3d effective cosmological constant $\Lambda_{eff}=-2\Omega/3>0$ which is independent of the integral constant. Here the scale factor is exponential expansion which is consistent with our present observation of the universe. Our results demonstrate that it is possible to construct a model which solves the dark energy problem, meanwhile guaranteeing a positive brane tension.